[R-sig-Geo] Support in krige/gstat

[Edzer Pebesma]

On 04/08/2011 12:40 PM, piero campa wrote:
> Dear list,
> I have datasets of different variables with different spatio-temporal
> supports, and I'd like to [co]krige them together.
> 
> What I'd like to ask you is:
> - I know that with block kriging one could estimate values over a different
> support area wrt the input variables, but is one allowed to have a disparity
> in the support areas among the input variables?

Theoretically there is no problem in doing this; there have been several
works doing this in the spatial domain, mostly named "area to point
kriging". Implementations seem to be done in matlab (by Phaedon
Kyriakidis), in ArcGIS (maybe not the current release but then probably
in the upcoming version) and in Pierre Goovaerts' software.

I don't know of any open source implementations, I also don't know about
implementations for the heterogeneous spatial AND temporal supports.

> - which is the right way to account for different spatio-*temporal* supports
> when [co]kriging data?

[Co]kriging is about solving systems with covariances between data and
prediction locations/areas, so the way to go is to estimate the
covariogram for the process on the point scale, and from there derive
the st/area-to-area covariances for any observation-observation or
observation-prediction pair by integrating, and put these in the kriging
equations. I believe the equations can be found as far back as in
Journel and Huijbregts' classic "Mining Geostatistics".

> 
> For what concerns the disparity in the *spatial* support, I'm assuming that
> the gstat library recognizes e.g. a SpatialPixelsDataFrame as a dataset with
> spatial support equal to the area of the pixels. But I'm not sure about
> this.

No, it doesn't; it assumes observations are points at pixel centers.

> For what concerns the different *temporal* support instead, I guess a
> spatio-temporal model needs to be built up.  (?)

generally speaking, yes; some people also use 3-D variogram models for
space time (taking the S/T anisotropy issue into account of course).

> 
> Really thank you for the support.

;-)

> Regards,
> /Piero
> 
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-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
http://www.52north.org/geostatistics      e.pebesma at wwu.de